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Bosonizations of quantum linear spaces are a large class of pointed Hopfalgebras that include the Taft algebras and their generalizations. We giveconditions for the smash product of an associative algebra with a bosonizationof a quantum linear space to be (semi)prime. These are then used to determine(semi)primeness of certain smash products with quantum affine spaces. Thisextends Bergen's work on Taft algebras.

Prime and semiprime quantum linear space smash products